Question

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Data on the last three years of demand are available as follows: Year Three years ago Two years ago Last year Spring 18 26 34 Season Summer 10 18 26 Fall 26 34 42 Winter 42 50 58 What is this year's seasonally adjusted forecast for each season?

Answer 1

Solution:

Step 1: First, find the year wise average value and overall average value as mentioned below:

Year Wise Sales Season t-2 t-1 t-3 18 26 18 10 Spring Summer Fall Winter Total 34 26 42 58 34 26 42 96 50 128 160 Avg (Total/4) 24 32 40 Overall Avg Value 32

Where t = Current Year and Overall Value = Sum of Average Values / 3

Step 2: Find year-wise seasonal factors as mentioned below:

Seasonal Factor = Actual Value for Season 'X' of year 'Y'/ Average yearly value of year 'Y"

Where X = Spring, Summer, Fall, Winter, and Y= year t-1, t-2, and t-3

Hence, we get the following table showing year-wise seasonal factors:

Season Total Spring Summer Fall Year wise seasonal factors t-3 t-2 t-1 0.7500 0.8125 0.8500 0.4167 0.5625 0.6500 1.0833 1.0625 1.0500 1.7500 1.5625 1.4500 2.4125 1.6292 3.1958 4.7625 Winter

(Rounded to 4 decimal places)

Step 3: Find the column of Seasonality Indices:

Seasonality Index for a particular Season = Total of Seasonality Factor for that particular Season / 3

Hence, we get the following table:

Season Total Spring Summer Fall Year wise seasonal factors t-3 t-2 t-1 0.7500 0.8125 0.8500 0.4167 0.5625 0.6500 1.0833 1.0625 1.0500 1.7500 1.5625 1.4500 2.4125 1.6292 3.1958 4.7625 Seasonal Indices 0.8042 0.5431 1.0653 1.5875 Winter

Step 4: Forecast the seasonal sales for all the seasons of this year (t):

Seasonal forecast for a particular season of this year (t) = Seasonality Index for that particular season X Average seasonal value for this year

As there is no specific information given in the question, regarding the total or average expected value for this year, we will take an overall average = 32 as an average seasonal value for this year.

Hence, we get the seasonal forecasts for all four seasons of this year as mentioned in the below table:

Season Total 2.4125 Spring Summer Fall Year wise seasonal factors t-3 t-2 t-1 0.7500 0.8125 0.8500 0.4167 0.5625 0.6500 1.0833 1.0625 1.0500 1.7500 1.5625 1.4500 Seasonal Indices 0.8042 0.5431 1.0653 1.5875 Seasonal Forecast for This Year 25.73 17.38 34.09 50.80 1.6292 3.1958 4.7625 Winter

(Rounded to 2 decimal places)

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